Tool for finishing tapered gears and method of finishing such gears



Spt; 23, 1-941. E. WILDHABIER v TOOL FOR FINISHING TAPERED GEARS AND METHOD OF FINISHING SUCH GEARS Filed April 15, 193:5.

Sept. 23, 1941. E. WILDHABER 2,256,586'

TOOL FOR FINISHING TAPERED GEARS AND METHOD OF FINISHING SUCH GEARS Filed A ril 1:5, 1935 2 Sheets-Sheet 2 Patented Sept. 23, 1941 METHOD QE FINISHING SUCH GEARS Ernest Wildhaber, Rochester, N. Y., assignor to Gleason Works, Rochester, N.'Y., a corporation of New York Application April 13, 1933, Serial No. 665,949

34 Claims.

The present invention relates to tools and to a process for finishing gears and particularly to tools and to a process for finishing spiral bevel and hypoid gears. The invention isapplicable to various types of finishing processes and tools. Thus, it may be applied in burnishing, lapping, shaving, finish-cutting, etc.

Because of the sliding action between gears whichjmesh with angularly disposed, offset axes, attempts have been made before to burnish or lap spiral bevel gears with hypoids. Where a single hypoid pinion or gear has been used, however; re-

suits have not been successful. A hypoid finishing gear as heretofore designed has not been capable of completely rolling out or sweeping .both side surfaces of the teeth of a spiral bevel gear or pinion. Hence, ithas been proposed to lap or burnish a spiral bevel gear or pinion by meshing it with a pair of hypoid pinions or gears, where each hypoid pinion or gear was constructings, in which:

ed so as to finish one side of the teeth of the gear 7 or pinion being burnished or lapped. This methcd also has. not proved commercially-successful to date, because of the difliculty and cost of making a pair of hypoid pinions or gears which will mesh simultaneously with a gear or pinion. v

The primary purpose of the present invention is to provide an improved gear-shaped finishing tool of hypoid form which will be suited to finish both sides of the teeth of a tapered pinion or gear blank either simultaneously orsuccessively and which will be capable of engaging said sides to the full extent to which they are 'engaged'by a mating gear.

It is' a further object of the present invention to provide a finishing tool of the character described which is capable of engaging both sides of the teeth of a tapered gear blank on their full length in a'single bodily position,

A still further object of the invention is to provide a finishing tool whose active tooth surfaces are free from undercut.

Still another object of the invention is to provide a finishing tool of the character described which can be accurately ground and which can be resharpened in such manner that it will continue to produce completely identical .gears throughout its whole useful life.

The invention'is not limited to the formation of bevel gearing, but may be employed success. fully, also, in the finishing of hypoid gearing. In

general, it is the purpose of the invention to provide an improved form of gear-shaped tool which will mesh with a bevel gearvor pinion in ofizset 'regiven spiral bevel lation and toprovide an improved, form of gearshaped tool which may mesh with a hypoid gear,

or pinion with its axis more offset from the axis of the gear or pinion than is the axis of the mating hypoid pinion or gear when the pair are in mesh. i

' Tools constructed according tovention may or may not be provided withcutting edges depending upon their use. If provided with cutting edges the portions back of the cuttin edges need not in all cases'be relieved, but may lie in the same tooth surfaces inwhich the cutting edges lie.

Several different embodiments of the invention have been illustrated in the accompanying draw-' Figure 1 is a view taken in a plane tangent to the pitch surfaces of a pair of spiral bevel gears and illustrating diagrammatically the'mesh of such gears and the relation between the pair and a finishing tool constructed according to the present invention for forming one member of the. pair;

Figure 2 is a fragmentary view showing the pair of spiral bevel gears referred to in Figure '1 in mesh and indicating, also, the position of the axis of the finishing tool. The larger member of the pair is shown in axial section and the pinion or smaller member-of the pair is shown in side elevation with a part broken away;

Figure 3 is a'diagram further illustrative of the relation between the spiral bevel pinion referred to in Figure 1 and shown in Figure 2 and a finishing tool for forming the tooth surfaces of said pinion according to the present invention:

Figure 4 is a front view showing the spiral bevel pinion and finishing tool in operative engagement;

Figure '5 is another view of the tool and pinion illustrated in Figure 4, this view being taken in the direction of the tool axis; I

Figure 6 is still another view of the tool and pinion shown in Figures 4 and 5, this view being taken in a direction perpendicular to the axes of the'pinion and of the finishing tool and the finishing tool being shown partly in section;

Figure .7 is a fragmentary sectional view of a modified form of finishing tool; v

Figure 8 is"a fragmentary plan view of the spiralbevel gear of Figure 2 and of the tool for finishing the same according to the present invention;

Figure 9 is a view taken at right angles to Figure 8 and showing the-tool in side elevation the present in- I i the gear.

and the spiral bevel gear in axial section, both tool and gear being shown fragmentarilyr Figureglo'is a fragmentary axial section of a modified form of tool for finishing spiral bevel gears according to the present invention;

Figure 11 is a diagrammatic view illustrating the comparative profile meshing action between a bevel pinionand its mating bevel gear and between the same pinion and an ordinary hypoid Figure 12 is a similar diagram illustrating the mesh offa bevel gear with its mating pinion and with an ordinary hypoid pinion; and

Figures 13, 14 and 15 are normal sections taken adjacent the large end, the center and the small end, respectively, of a tooth of a tool constructed according to the present invention.

In designing conventional hypoid gears, different pressure angles are provided on opposite sides of the teeth of-both members of the pair in order to obtain good action on both sides of the teeth. 80, for instance, a pressure angle of I'l /2 or of 14%? may be used on the drive side of a conventional hypoid rear axle gear where the pinion is below center, whereas on the coast side, a pressure angle of 25? may be used and, when the pinion is set above center, conditions are reversed. Oneof the problems, which has been solved by the present invention, hasbeen to design a rotarycutting tool of gear form which is to engage in slidingmesh with a given tapered gear, for instance, a bevel gear or pinion, which will have the same normal pressure angle on bothsides of its teeth in correspondence to those of the bevel sear or pinion and which will rotate with the given gear or pinion without producing an undercutting action and which at the same timewill have sufficient profile action to completely roll out the teeth of the given gear or pinion.

In Figure 1, III designates a fragment of the developed pitch surface of a spiral bevel gear or,

pinion, constituting one member of the pair shown in If'lgureil. This pair consists of the pinion and gear 23. These gears rotate on axes 2i and 2|,respectively, which extend at right angles to'one another and which intersect in their "common apex 20.

In Figure 1. theline 21 designates a pitch line .elementof the gear shown namely, the line formed by'the intersection of the pitch surface with the side of a tooth of said gear. This line 2-1 is a circular arc, whom center is at a. The

mean inclination It 'oi' the curve 21 with respect to a generatrix' iroffthe pitch surface of the gear rpinion is known as the spiral angle of To for-ma cated, the spiral angle h of the teeth of the tool gear, which are to match those of the spiral bevel gear or pinion, is larger than the spiral angle h of thespiral bevel pair.

As is well known, the mesh between a pair of bevel gears takes place along the surface of action, which passes ,through the instantaneous axis of the gears, that is, through the contact line of their conical pitch surfaces, and which adjacent said instantaneous axis is perpendicular to the contacting tooth surfaces. The determination of this surface of action is well known.

' Adjacent the instantaneous axis it contains the tooth normals which intersect the instantaneous axis. The inclination of the surface of action with respect to the pitch plane, that is, with respect to the plane tangent to the pitch surfaces of the pair'of gears, depends, therefore, on the inclination of the tooth normals to the sides of the teeth of the gear, namely, on the pressure angles of the tooth surfaces of the gears. If we assume for the sake of explanation, that we have a. pair of bevel gears in which the inclination or pressure angle of the tooth surfaces is zero, the inclination of the surface of action of the pair of gears will also be zero, of course, a pair of bevel gears in which the tooth surfaces are of zero pressure angle will not operate. The actual pressure angle of a pair of bevel gears must differ substantially from zero.

Let us refer now to Figure 11, which is a circumferential section of a. bevel pinion, for in-, stance, a spiral bevel pinion. The profile designated at may be, for instance, the mean pro file of a concave tooth side of the spiral bevel pinion 22 of Figure 2. In the section shown in Figur 11, the line of action between the pinion teeth and the teeth of the mate gear is designated at 36. It is inclined to the pitch plane 31 at an angle a equal to the circumferential pressure angle of'the tooth profile 35.

Ordinarily, the line of action 38 is nearly straight. It is tangent to the base circle 38 of the profile 35.

,The rolling action of the profile 35 with mating profiles of the mate gear ,2! ends at the point e 39 of tangency ofthe line of action 38 with the bevel gear or pinion according to: the'present -invention,fa, finishing tool is ,pro-

vvided which meshes: with its axis offset from 'the'arls' of the Bear-or "pinion and inclinedto the 'axisof the "gearor pinion preferably at an angle different from the angle between the axes of the'paii' when in mesh.- This tool is, moreover,

preferablyprovided' with teeth of larger spiral angle than thespiral angle of the gear or pinion g bs finished. "Thus, as shown in Figures 1' and :2, the axis'll'of thetool for finishingthe pinion II is ofi'set from; the axes 2| and .of the gear :atidpifloltand preferably inclined, as shown in me}; at other than a. right angle to the axes base circle 38, or broadly, at the point]! closest to the axis 24 of the pinion. Accordingly, the,

active profile 35 of the pinion tooth terminates at the point 40 which lies on the base circle I. and corresponds to the point 39 at a different angular position of the pinion. V

As indicated above, it is quite possible tov form a hypoid gear which will be conjugate to a bevel pinion 22 and which will mesh with said pinion with its axis ofl'set from and angularly disposed to the enact the pinion. When the hypoid gear is .madein usual manner, however, its teeth will mesh with the teeth of the pinion 22 along a line of action, such as the line 36', which is different from the line of action 38 between the pinion and its mate gear.

In Figure 11, the line of action as is shown as j inclined to the pitch plane at an angle smaller than-the angle 0. Usually. the lineof action between'the teeth of a conventional hypoid gear and the mating tooth surfaces of a bevel pinion f will be inclined to the pitch plane at a, smaller -in=this figure indicates the projection of the gear axis to the pitch plane. As indiangle-than the pressure angle a on one side of.

the teeth and at a'largenangl'e on the other side of the teeth. 7

It is clear that if the Pinion I2 mesheswith the hypoid gear along'a line of action ll, the

teeth of the hypoid gear cannot sweep-the wholeacsopee 3 pinion profile from the tip down to the point where tooth action between the profile 35 and the profile of a tooth of a mating gear ends, In fact, the tooth surfaces of the hypoid gear will only roll over the tooth profile 35 as far as the point 4| which corresponds to the point 42 of tangency of the line of action 33 with the circle 43 circumscribed about the gear axis 24 as a center.

A hypoid tool gear of conventional form is, therefore, unsuited to completely sweep out both sides of the teeth of a given bevel pinion or gear. This is true even when the line of action between the hypoid gear and the spiral bevel gear extends across the whole of the tooth zone of the bevel gear.

Figure 12 illustrates the latter type of mesh. The line of action between a tooth profile 44 of the gear 23 and tooth surfaces of the mating pinion 22 is inclined at an angle a to the pitch plane 31, which is equal to the angle a of Figure .11, because the pressure angles of a pair of mating spiral bevel gears are equal. The line of action between the gear 23 and a conjugate hypoid pinion of conventional structure is indicated at 45'. This line of action 45' is assumed to extend across the whole of the tooth zone or the gear 23, that is, this line 45' is assumed to be tangent to the base circle (not shown) of the gear at a point (not shown) which is closer to the center of the gear than is the innermost point of the tooth profile 44. The are 45 denotes the external surface of the pinion 22 which meshes I with the gear 23. This are intersects the line of action 45 between pinion and gear at the point 41 which, therefore, marks the end of the active tooth profile of a tooth of the gear. The active portion of the tooth profile 44 extends, therefore,

toward the root of the tooth as far as the point 48, which corresponds tothe point 41.

If the hypoid pinion being used as a tool to finish the gear 23 has the same external outline 45, the active profile generated on the gear 23 will end at the point 49 which corresponds to the point 50 of intersection of the are 45 with the line of action 45' between the hypoid pinion and the gear 23. Hence, in this illustrated case, also; the profile of the tooth of the gear would be generated for only a part of its length by a hypoid pinion of conventional'construction.

Even if the diameter or the hypoid tool were increased with the purpose of generating the tooth profile 44 further down to its root, it would ordinarily be found that the line of action 45' between the hypoid pinion and the gear 23 would be changed by this increase in diameter of the hypoid pinion in such a way that its inclination to the pitch plane 31 would be reduced. Ordinarily, therefore, nothing would be gained by this increase in diameter of the tool-pinion.

The present invention rests upon the design I of hypoid tool-gears and tool-pinions whose lines of action are substantially equal to the lines" of action of the bevel gear pair or whose lines of action differ from the lines of action of the bevel gear pair by .so small an amount as to still allow of generation by the same tool of both sides of the teeth of the spiral bevel gear or pinion for the whole active height of the teeth.

This is accomplished by so designing the hypoid tool that if its pressure angle were reduced to zero, the line of action between the tool and the gear or pinion being finished would have approximately zero inclination to the pitch plane, just as is the case with bevel gearing, Ordinarily in hypoid gearing, the pressure angle, which corresponds to zero inclination of the line of action, differs generally from zero, sometimes by as much as 15. The actual pressure angle of a hypoid tool made according to the present invention is of course not zero, but the design of the hypoid tool is so determined in the present invention from the given design of the bevel member to be finished, that, as stated, were the pressure angle zero, it would correspond to a zero inclination of the line-of action. In this case, the lines of action between a bevel pinion or gear and a hypoid tool are substantially the same as the lines of action between said bevel pinion or gear and its mating gear or pinion.

Zero inclination of the line of action means that for. an infinitesimal distance, a point of contact between mating tooth surfaces of a spiral bevel pinion or gear and the hypoid tool will remain in the pitch plane as the spiral bevel pinion or gear and the hypoid tool rotate together. Thus, with zero inclination of the line of action, a mean point of contact would remain in contact with the hypoid member while the spiral bevel pinion or gear were being turned about its axis through an infinitesimal angle.

' the pinion has been turned through an infinitesimal distance as it rotates with the hypoid tool.

The tooth normal 55' at point 55' is inclined to-its original position 55 at-mean contact point 55 because of the infinitesimal turning movement of the pinion. Now, the turning motion f about the axis of the pinion can be resolved into a component (f cos y) coinciding with the pitch generatrix 2'9 and into a component (I sin 9) perpendicular to the pitch plane. The angle 9 is the pitch angle of the pinion.

If the point 55' is a point of mesh between the pinion 22 and the hypoid tool 51, then a unit force acting along the normal 55' must exert the same turning moment on the hypoid member as a unit force extending along the normal 55. Assuming still, for the purposes of explanation, that the pressure angle is zero, a component (1 cos y) will have no influence on the turning moment exerted, because this component is in the direction of the generatrix 29.

component acting, perpendicular to the pitch plane.

A unit force extending along the normal 55' n has naturally the same leverage with respect to the cone center 29 of the pinion as has a unit force extending along the normal 55. The leverage equals the radius of the circle 58, that is, the distance 25-59. To determine the required position of the apex of the hypoid tool 51, we may assume various positions of this apex and vwe find that the leverage of the two forces along 55 and along 55' is the same when the apex 50 of the tool-gear 5! lies on ,the line 25-59, whereas it differs for any other position, such as, the position 50' or 50".

Hence, if we select the hypoid tool 51 so that its apex 50 will lie on the line 2559 drawn through the pinion apex 25 parallel to the tan gent, 5! to the tooth 21 -at the mean contact point 55, we will have succeeded n so determinas shown in Figures 4, and 6.

ing a hypoid gear that zero inclination of the line of action will correspond to zero pressure angle as is the case with bevel gears. This means,

that when actual pressure angles are provided on the teeth of the hypoid tool, the inclination.

of the lines of action will be substantially the same as on the bevel gear pair itself.

The above -method of determination applies equally to hypoid tools for either gear or pinion and it enables us to design hypoid members capable'of meshing with both sides of a given bevel pinion or gear in such manner that the active tooth profiles and active tooth surfaces of the bevel gears are swept to their full extent.- It also enables us to provide tooth surfaces on the hypoid member which for their active height are free of undercut.

The hypoid tool is preferably so constructed that its teeth may mesh with the teeth of the bevel gear or pinion along their whole length in a single bodily position. However, if so desired, mismatch may be provided between the teeth of the tool and the bevel gear or pinion, as is usually provided on spiral bevel gears. In this case, the forming tool will be moved slightly in and out oftheoretically correct position during the forming operation.

In principle, the teeth of the forming tool may be directly generated conjugate to the given bevel gear,

The above rules are particularly true for gearing,produced with face mill cutters and they also facilitate the production of the forming members on existing hypoid generators.

In Figures 8 and 9 I have shown the gear 23 and a hypoid forming tool 65 for producing this The dimensions of the tool 65 are determined on the same general principles as above described withreference to determination of the pinion-tool 51. However, in certain respects, the hypoid todl for-forming the gear of the spiral bevel pair is preferably made different from the ber of teeth in the pinion 22 which mates with numbers N' and n of the hypoid tool and the bevel blank, respectively, their pitch angles G, g,

respectively, and the above mentioned leverage (A cos h) and (A 005 h) of the normal 56 with respect to the apex 60 of the tool and apex 26 of the gear:

(A cos it) sin G 1L (A cos h) simg n This equation simply expresses the relation that the normal pitch at the point must be the same on the forming member as on thebevel gear or pinion to'be formed.

The pitch angle G of a forming member 51 for a spiral bevel pinion 22 or. a skew bevel pinion is preferably made at least 10 smaller than the pitch angle G of the mating gear 23 of the spiral bevel or skew bevel pinion, so that in the forming operation, the finishing tool 51 and the spiral bevel pinion 22 will be mounted on axes disposed at an acute .angle to each other, The spiral angle 7:. of the tool gear 51 is preferably at least 8 different from the spiral angle h of the pinion to be finished and is preferably at least that-much larger than the spiral angle h' of the pinion to be finished. The spiral angle of the 1 tool gear may be up to 20 larger than that 1 of the pinion, but is usually between 8 and 16 1 larger. V 3 ing .tool 51 is preferably smaller by at least 20% than the number of teeth in the mating gear The number of teeth 6| in the form- 23, but, preferably exceeding the number of teeth in the pinion 22 which is to be formed.

its axis is disposed at a larger angle to the axis of the gear than the angle between the axis of the gear and the axis of its mate pinion when in mesh.

The number of teeth 61 .in the gear. forming tool 65 is preferably larger than the numthe gear and the spiral angle of the teeth of the forming gear tool also preferably exceeds the spiral angle h of the bevel pinion or gear by at least 8 and up to 20. If the hypoid forming tool is to be produced on existing hypoid, gear generators with a tool having a conical cutting surface or grinding surface, the pitch angle of the forming tool should be made considerably smaller than the pitch angle of the basic gear, which --the cutting or grinding tool represents injh'e" generating oper ation. The purpose of this is to avoid. concave profile curvatures on the forming member.

In the usual process of generating hypoid gears, the cutting or grinding tool represents a'" Figure 10 illustrates a modified form of finish- 1 ing tool, particularly intended for use when the gear to be finished is non-generated and especially when the tooth surfaces of this gear are surfaces of revolution, such as conical surfaces.

Here, the hypoid forming member 10 is provided with teeth 1| whichare of parallel depth, that is, which are of uniform height throughout their length. The tooth surfaces of such a form- 'ing tool 16 can 'be produced very simply and very accurately. -A face mill cutter ora grinding wheel having a working surface corresponding to the tooth surfacev of the non-generated gear is so positioned with reference to the'forming tool blank that the eutteror grinding wheel covers and describes the tooth surface of the non-generated gear which it is subsequently to finish, and at the same time a generating motion is produced between the cutter or grinding wheel and the forming tool blank as though said form ing tool 10 were meshing withthe non-generated gear. Tooth surfaces will thereby be generated on the forming tool blank which are truly conjugate to the tooth surfaces of the mate non-generated gear and which, when meshed with a non-generated gear to be finished, will produce tooth surfaces of mathematical accuracy upon the non-generated gear.

A forming tool constructed according to the present invention and the spiral bevel gear or pinion to be finished thereby may be considered as a pairof hypoid gears. They differ, however,

from a hypoid gear pair of conventional design in the first place in having substantially equal pressure angles and also comparatively low pressure angles (smaller than 18) on both sides of the teeth. So long as the offset between the axis of the hypoid tool and the spiral bevel gear or pinion to be finished thereby is not excessive, or the difference in their spiral angles is not too great; the new design of hypoid finishing tool permits of completely sweeping out both sides of the teeth of the bevel gear Qrpinion.

The tooth surfaces of tools made according to the present invention have tooth profiles changing lengthwise of the teeth, as is the case with bevel or hypoid gears. The average pressure angles of the tools are substantially the same on both sides of the teeth and generally the pressure angles decrease from the large end to the small end of the teeth on both sides of the teeth.

Figures 13, '14 and are enlarged normal sections of a tooth 6| of the tool 51. As is seen,

the pressure angles out the sides 10 and 'II of the tooth are equal at the large end of the tooth, the pressure angles 0 of the sides I0 and H of the tooth are equal midway the length of the tooth, and likewise the pressure angles d ofthe sides 10 and H of the tooth at its small end are equal, but the pressure angle of each side decreases from the large to the small end of the tooth. Thus, the pressure angles 17 at the large end of the tooth are larger than the pressure angles 0 at the center of the tooth and the pressure angles 0, in turn, are larger than the pressure angles d at the small end of the tooth. It will be noted, further, that the profiles of the sides 10 and Il change along the length of the teeth. The same characteristic of tooth shape and pressure angle is to be found in the tool 65.

In hypoid gears of conventional design, the

I, pressure angles are nearly constant along the teeth, and, if they do change a little, they change in opposite directions on the two sides. Inother words, if on one side, the pressure angles decrease from the large end to the small end of the tooth, they increase on the other side from the large to the small end of the tooth. If the tools 51 and 65 are to be used for bur- .nishing or lapping, their tooth surfaces are left smooth. In such case, the tools will resemble ordinary gears. If the tools are to be used for shaving, however, the tooth surfaces are notched or grooved or, in fact, actual flutes may be'cut through the teeth of the tools to provide the shaving action. One way in which the teeth of ,8- tool may be formed to provide a shaving action isshown in Figure 5. In this case, one of the teeth ii of the tools'l is shown formed with grooves 12 in its side tooth surfaces. These grooves 12 are provided on both sides of the teeth. For ordinary shaving work, the lands 13 between the grooves will lie in the original tooth surfaces of the tools and the cutting or shaving action is produced simply by the slidingaction of the tool and gear to be shaved in mesh. The

grooves 12 may be formed in any suitable man-' ner, as, for instance, by milling these grooves in the sides of the teeth after the teeth have been formed.

If a cleaner cutting action is desired, the lands 13 may be relieved back of their front edges so that only the front edges of the lands willlie in the original tooth surfaces and these edges will then operate as actual cutting edges.

Only one of the teeth of the tool 51 in Figure 5 is shown as grooved, but it will be understood, of course, that if the tool is to be used for shaving, allof the teeth will be so formed. On the other hand, if the tool is intended for lapping and burnishing, all of the teeth will be smooth, as are the two teeth indicated as 8|.

In bumishing, lapping, shaving or cutting a gear with a. tool made according to the present invention, the tool and the gear which is to be finished are mounted in correct meshing relation with their axes offset and inclined to one gear or pinion is to be lapped, provision should be made for applying the lapping compound to the gear, unless it isintended to put the compound on by a brush. a

To sharpen a shaving tool made according to the present invention, all that is required is to grind back the tooth sidesand top and then advance the tool axially enough to compensate for the stock removed in the sharpening. operation'. The sharpening operation can be effected on a spiral bevel gear grinder of the generating type. Of course, the'sharpening of the tool reduces its outside diameter, but ordinarily, the teeth of a shaving tool are not sharpened back to any great depth. Hence, if the face width of the shaving tool is made sufliciently large initially, the same effective outside diameter can be maintained throughout the whole life of the tool, as the tool is advanced axially aftereach sharpening.

Where tools constructed according to the present invention are to be used for lapping, it may be desirable at intervals to refinish the lapping tooth surfaces so as, to maintain the desired,

thickness of tooth. In this case, the tool can be used longer by not only grinding .back its tooth sides, but also deepening v the bottoms of the tooth slots and then advancing the tool axially to compensate for the stock removed.

In this case. it might not be practical in all in- Y stances to make the tool of suflicient face width. initially that the effective outside diameter would remain constant despite the axial advance. In many instances, therefore, it may be desirable to make the lapping tool of the form shown in Figure 7. Here a tool I5 is sho'wn,'which in original form is of considerable depth axially. The-outer ends of the teeth 16 of this tool lie in a cylindrical surface 11 which is coaxial with the axis]! of the tool. This tool can be refinished by grinding back the sides of its teeth 16 and by grinding the bottom 'IQ of its tooth slots to greater depth, as indicated atli', 19"

disposed I the axis of said bevel gear, saidtool having teeth etc. Due to the fact that the surface 11 is cylindrical and coaxial with the tool, this tool can be advanced axially, after refinishing, without whose pressure angles decrease from the large end to the small end of its teeth on both sides.

7. A tool of gear form for finishi'ngtapered gears, said tool being adapted to mesh with the uses or embodiments of the invention following,

in general, the principles-of the invention and including such departures from the present disclosure as come within known or customary practice in the gear art and as may be applied to the essential features hereinbefore set forth and as fall within the scope of the invention or the limits of the appended claims.

Having thus described my invention, what 1 claim is:

1. A tool of gear form for finishing tapered gears, said tool being adapted to mesh with a tapered gear with its axis offset from and angularly disposed to the axis of the tapered gear,

. said tool having teeth curved longitudinally along circular arcs in development and tooth surfaces of approximately the same normal pressure angle on both sides of the teeth at any point along the tooth length. I

2. A tool of gear form for finishing tapered gears, said tool having teeth curved longitudinally along circular arcs in development whose spiral angle is larger thanthe spiral angle of'the teeth of; the tapered gear to be produced, said tool having tooth surfaces of approximately the same normal pressure angle on both sides of the teeth at any point along the tooth length and being adapted to mesh with a tapered gear with its axis oifset from and angularly disposed to the axis of the tapered gear.

3. A tool of gear form for finishing one member of a pair of tapered gears, said tool havin tooth surfaces whose normal pressure angles are approximately the same on both sides of a-tooth Y at any point along its length and being adapted -'to mesh with its axis ofi'set from the axis of the gear to be finished and disposed to the latter axis at a difierent angle from the angle between theaxes of the two members of the pair when in mesh.

4. A tool of ber ofa pair of tapered gears, said tool having tooth surfaces whose normal pressure angles decrease from the large to the small end of the teeth on both sides of the teeth and being adapted to mesh-with its axis ofiset from the ,axis of the gear to be finished and disposed to the latter axis at a diflferent angle from the angle between the axes of the two members of the pair when in mesh.

'5. A tool of gear form for finishing a tapered gear, said tool having approximately equal, normal pressure angles and approximately like pro file curvature on both sides of its teeth but having diiferent normal pressure angles and difierent profiiecurvatures at different points along their length, and said tool being adapted to mesh with the gear to be finished with its axis offset from and angularly disposed to the axis of the ear to be finished.

6. A tool of gear form for finishing ,a bevel gear, said tool being colliugate to a bevel gear gear form for finishing one memwhose tooth surfaces are'de'rived from a surface ear to be finished with-its axis oilset from and angularly disposed to the axis of the tapered gear, said tool having teeth whose pressure angles increase on both sides measured from the small end to the largeend of the .teeth. 8. A tool of gear form for finishing tapered gears, said tool being adapted to mesh with the gear to be finished with its axis ofiset from andv angularly disposed to the axis of said gear, said tool having teeth whose pressure angles increase at, approximately the samerate on both sides measured from the small end to the large end of the teeth.

9. A tool of gear form for finishing tapered gears whose teeth are curved longitudinally alongcircular arcs in development, ,said tool being adapted to mesh with the gear to be finished with its axis offset from and angularly disposed to the axis of said gear, the tool having teethcurved longitudinally along circular arcs in development, each tooth having pressure angles increas. ing from the small end to the large end of the teeth'on'both sides of the teeth.

10. A tool of gear form i'or finishing tapered gears having teeth curved longitudinally 'along' circular arcs in development, said tool being adapted to mesh with the gear to be finished with its axis oflset from and angularly disposed to the axis of said gear, said toolhaving teeth curved longitudinally along circular arcs in development, each tooth having pressure angles increasing at approximately the same rate on both sides measured from the small end to the large end of the teeth. i a

11. A tool of gear form for finishing one member of. a pair of tapered gears, said tool having teeth whose pressure angles increase from one end of the teeth to the other on both sides of the teeth measured in the same direction,'said tool being adapted to mesh with the gear-to be finished with its axis angularly disposed to the axis of the gear to be finished and oiiset more from the axis of said gear than is the axis of its mate gear when the pair are in mesh. 12. A tool of gear form for finishing one member of a pairof tapered gears, said tool having teeth whose pressure angles increase from the small end tothe large end of the teeth on both sides of the teeth, said tool being adapted to mesh with the gear to be finished with its axis angularly disposed to the axisofsaid gear and onset more from the axis of said gear than is the'axls of themate gear when the pair are in mesh. 13. -A tool of gear form for finishing one mem .ber of a pair of tapered gears, said tool having teeth whose pressure angles increase zit-approx-- imately the same rate on both sides of the teeth measured from the small end to the large end ofthe teeth, said tool being adapted to mesh with the gear. to be finished with its axis anber of'a pair of tapered gears' which have teeth curved longitudinally along circular arcs in development, said tool; having teeth curvedlongh tudinally alongcircular arcs in development,

each tooth having its pressure angles increasing from the small end of the tooth to the large end thereof on both sides of the tooth, and said tool being adapted to mesh with the gear to be finished with its axis angularly disposed to the axis of said gear and offset more from the axis of said gear than is the axis of its mate when. the pair are in mesh.

15. The method of finishing a tapered gear which comprises meshing a tool of tapered gear form with the tapered gear with the axis of the tool oflset from the axis of the tapered gear and with the apex of the tool lying on a line passing through the apex of the gear and parallel to a tangent to the tooth surface of the gear at a mean point of contact between the tool and gear, and rotating the tool and gear together.

16. A tool of gear form for finishing one member of a pair of tapered gears, said tool having teeth the pressure angles ofwhose side tooth surfaces increase from the small end to the large end of the teeth on both sides of the teeth, said tool having a different number of teeth from the mate of the gear to be finished and meshing with the gear to be finished with its axis offset from and angularly disposed to the axis of said gear. 4 v

17. A tool for finishing spiral bevel gears,

which is of hypoid gear form and is adapted to mesh with its axis ofl'set from and angularly disposed to the axis of a bevel gear, and which has teeth of the same pressure angles on opposite sides at any point along its length but of decreasing pressure angles from the large to the small end of its teeth.

8. A tool for finishing, spiral bevel gears, which is of hypoid gear form adapted to mesh with the gear to be finished with its axis offset from and angularly disposed to the axis of saidgear, and which has teeth of substantially equal pressure angles on opposite sides at any point along its length, but of decreasing pressure angles from the largeend to the small end of the teeth and of changing profile shape. A

19. A tool for finishing tapered gears l-which is of hypoid gear form adapted to mesh with the gear to be finished with its axis oflset.from the axis of said gear and which has teeth of'changfrom the number of teeth of the mate to the gear which is to be finished.

23. A tool of hypoid gear form for finishing tapered gears, having teeth whose tooth surfaces increase in pressure angle on both sides of the teeth from the small to the large ends of the teeth, and which is adapted to mesh with the gear to be finished with its axis disposed to the axis of said gear at an obtuse angle.

24. A tool of hypoid gear form for finishing tapered gears, having teeth whose spiral angle is larger than the spiral angle of the teeth of the gear to be finished and Whose tooth surfaces increase in pressure angle on both sides of the teeth from the small to the large end thereof and which is adapted to mesh with the gear to a be finished with its axis disposed to the axis of said gear at an obtuse angle. 7

25. A tool of hypoid gear form for finishing a tapered gear, said tool having teeth whose spiral angle is larger than the spiral angle of the gear. to be finished and whose pressure angle increases from the small to the large end of the teeth on both sides of. the teeth and whose pitch cone angle is different from the pitch cone angle of the mate of the gear to be finished.

26. A tool of hypoid gear form for finishing a tapered gear, said tool having teeth whose spiral angle is larger than the spiral angle of the teeth of the gear to be finished, and whose pressure angle increases fromthe small end to the large end of the teeth on both sides of the teeth, but

is approximately the same on both sides at any point along the length of the-teeth, and whose pitch coneangle is different from the pitch cone angle of the mate of the gear to be finished.

27. A. tool which isof tapered gear form for finishing tapered gears and which haslongitudi-v nally curved teeth that are of changing profile curvature from one end of the teeth to the'other and whose normal pressure angles decrease from the large to the small end of the teeth on both sides of the teeth.

mg profile from one end to the other and of the same normal pressure angles on both sides at any point along their length and of approximately 28. The method of finishing a pair of longitudinally curved tooth tapered gears, which have unequal numbers of teeth and which mesh with angularly disposed axes, which comprises finishing the smaller member of the pair by meshing with said smaller member a tool of tapered gear the same average pressure angle as the teethof the gear to be finished, but of decreasing pressure angles on'opposite sides from'the large to the small ends of the teeth.

20. A tool of hypoid gear form for finishing tapered gears, whose teethhave tooth surfaces decreasing in pressure angle on both'sides of the teeth from the large to the small ends of the teeth and'whose mean cone distance is less than that of the gear to be, finished. l

21. A tool of hypoid gear form for finishing tapered gears, whose teeth are of larger spiral angle than the spiral angle of the teeth of the gear to be finished'and whose tooth surfaces decrease' in pressure angle on both sides of the teeth from the large to the small ends of the teeth and whose mean. cone distance is less than that of the gear to be finished. l

22. A tool of hypoid gear form for finishing tapered gears, having teeth whose spiral angle is larger than the spiral angle of the teeth of the gear to be finished and whose tooth surfaces increase in pressure angle from the small end form with the axis of the tool offset from the axis of said smaller member and disposed to the axis of said smaller member at a smaller angle than the angle between the axes of the pair, and

rotating the tool and smaller member together, and finishing the larger member of the pair by meshlng with said larger I member a tool -of tapered gear form with the axis of the tool offset from the axis of the larger member and disposed to the-axis. of the larger member at an angle greater than the angle between the axes of the pair when in mesh, and rotating the second tool 'and the larger member together;

29. The method of finishing a pair of longitudinally curved tooth tapered gears, which have unequal numbers of teeth and which mesh with angularly disposed axes, which comprises finishing each member of the pair with a tool of tapered gear form that has longitudinally curved teeth whose spiral angle is greater than the spiral angle of the teeth of the gear to be finished but whose pressure angles are substantially the same on opposite sides of the teeth at any point along the length of the teeth but which are of decreasing pressure angle on both sides of the teeth from thelarge to the small end of the teeth, by

. meshing, in each instance, the tool with the gear the angle between the axes of the pair of gears when in mesh, and then rotating the tool and gear together, the tool used in finishing the larger member of the pair having a greater number of teeth than the smaller member the pair and having. its axis disposed at a greater angle to the axis of the larger member oi the pair than the angle between the axes of the pair, and the tool used in finishing the smaller member of the pair having a fewer number of teeththan the larger member of the pair and having its axis disposed at a smaller angle to the axis oi the smaller member of the pair than the angle between the axes of the pair.

,30. The method of finishing a pair of longitudinally curved tooth tapered gears, which have unequal numbers oi teeth and which mesh with axes atright angles, which comprises finishing each member of the pair with a tool of tapered gear form that has longitudinally curved teeth whose pressure angles decrease on both sides from thelarge to the small ends of the teeth, by

its axis disposed at an obtuse angle to the larger member 01' the pair, and the tool used in finishits teeth from end to end and the same normal pressure angle on both sides 01' its teeth at any point along the length 01' its teeth and which is adapted to mesh with .a mate gear with its axis meshing, in each instance, the tool with the Y gear to befinished-so that the axes oi tool and gear are oiiset from one another and angularly disposed to one another at an angle other than a right angle, and then rotating the tool and .gear together, thetool used in finishing the larger member 01' the pair having a smaller number 10! teeth than said member but having a greater number of teeth than the smaller member of thepair and having its axis disposed at an obtuse angle to the axis oi the larger member of the pair, and the tool used in finishing the smaller member of the pair. having a greater number of teeth than the smaller member but less teeth than the larger member of the-pair. and having its axis disposed at an acute angle to the axis of the smaller member.

31. The method 0! finishing a p ir oiv lon8i-' tudinally curved tooth tapered gears, which have unequal numbers oi teeth and which mesh with axes at right angles and intersecting. whichcomprises finishing each member of the pair with a tool oitapered sear form that has longitudinally curved teeth whose spiralangle is greater than the spiral angle of the teeth 01 the gear to be finished and whose pressure angles decrease on both sides of its teeth mm the large to the small end oi the teeth but are approximately the same on opposite sides oi its teeth at any point along the length of its teeth, by meshing, in each instance, the tool with the gear to be finished so that the axes oi'tool and sear are moreoiiset than the axes of the pair when in mesh and are angularly disposedrto one another at an angle other than a right angle, and then rotating the tool and gear together, the tool-used in finishing the larger member oi-the pair having less teeth than said member but a number of teeth than the smaller member of the pair and having angularly disposed to and intersecting the axis of the mate gear, which comprises employing a tool of tapered gear form that has longitudinally curved teeth whose spiral angle is greater than the spiral angle of the teeth of the gear which is to be finished but whose opposite sides have substantially the same normal pressure angle at any point along the length of the teeth but decreasing normal pressure angle on both sides from the large to thesmall end of the teeth, and meshing said tool with the gear which is to be finished with the axis of the tool ofl'set from and angularly disposed to the axis of the gear, and rotating the'tool and gear together on relatively fixed axes.

33. The method .0! finishing a tapered gear which has longitudinally curved teeth and which is adapted to mesh with its mate with its axis angularly disposed to the axisoi the mate, which comprises employing a tool of tapered gear form tudinally curved teeth whose pressure angles decrease on both sides from the large to the small ends oi its teeth, and meshing said tool with 40 the gear so that the axis of the tool is angularlydisposed to the axis of the gear and is more oilseti'rom the axis of the gear than are the axes of the gear and its mate when in mesh, and rotating the tool and gear together on relatively fixed axes.

-' 34. The method oi finishing a tapered gear which has longitudinally curved teeth and which is adapted to mesh with its mate with its axis angularly disposed to the axis of the mate, which comprisesemploying a tool of tapered gear form thatis suited to finish both sides of the gear simultaneously. said tool having longitudinally curved teeth whose pressure angles decrease on.

both sides from the large to the small ends of its teeth and havin a cone distance less than the cone distance of the gear to be finished, and meshing said toolwith the gear so that the axis of the tool is oii'set from the axis oi the gear and is inclined to the axis of the gear at an angle 'difierent from the angle between the axis of the gear and its mate when in mesh and so that the apex of the tool lies between the axis of the gear and the tooth zone of the tool, and-rotating the tool and gear together on relatively fixed 

